A Monte Carlo algorithm for studying phase transition in systems of hard rigid rods

Kundu, Joyjit; Rajesh, R.; Dhar, Deepak; Stilck, Jürgen F.

doi:10.1063/1.4709907

Cited by 30 publications

(45 citation statements)

References 4 publications

(4 reference statements)

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“…Additional support for this scenario comes from the fact that if the hard-core constraint is relaxed, and two k-mers are allowed to share a site, but with a cost in energy, then exact calculation on an artificial lattice (the random locally tree-like-layered lattice) shows [31] two phase transitions at densities ρ c1 and ρ c2 for a range of values of the repulsive energy. The difference between these critical densities decreases as the repulsive energy is decreased, and below a particular value of the repulsive energy, the intermediate nematic phase disappears.…”

Section: Summary and Discussionmentioning

confidence: 99%

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Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

et al. 2013

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We study the phase transition from a nematic phase to a high-density disordered phase in systems of long rigid rods of length k on the square and triangular lattices. We use an efficient Monte Carlo scheme that partly overcomes the problem of very large relaxation times of nearly jammed configurations. The existence of a continuous transition is observed on both lattices for k = 7. We study correlations in the high-density disordered phase, and we find evidence of a crossover length scale ξ * 1400, on the square lattice. For distances smaller than ξ * , correlations appear to decay algebraically. Our best estimates of the critical exponents differ from those of the Ising model, but we cannot rule out a crossover to Ising universality class at length scales ≫ ξ * . On the triangular lattice, the critical exponents are consistent with those of the two dimensional three-state Potts universality class.

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Section: Summary and Discussionmentioning

confidence: 99%

“…The Monte-Carlo algorithm we use is defined as follows (this was reported earlier in a conference [21]): given a valid configuration, first, all x-mers are removed without moving any of the y-mers. Each row now consists of sets of contiguous empty sites, separated from each other by sites occupied by y-mers.…”

Section: Model and The Monte Carlo Algorithmmentioning

confidence: 99%

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

et al. 2013

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“…The algorithm presented in Refs. [13,20] is generalizable to the case when intersections are allowed. Confirming whether the qualitative behavior is similar to that seen for RLTL would be interesting.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The existence of this transition has been has been proved rigorously for large k [12]. The second transition from nematic to HDD phase was studied using an efficient algorithm that ensures equilibration of the system at densities close to full packing [13,20]. On the square lattice the second transition is continuous with effective critical exponents that are different from the two dimensional Ising exponents, though a crossover to the Ising universality class at larger length scales could not be ruled out [13].…”

Section: Introductionmentioning

confidence: 99%

Reentrant disordered phase in a system of repulsive rods on a Bethe-like lattice

Kundu

Rajesh

2013

Phys. Rev. E

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We solve exactly a model of monodispersed rigid rods of length k with repulsive interactions on the random locally tree like layered lattice. For k ≥ 4 we show that with increasing density, the system undergoes two phase transitions: first from a low density disordered phase to an intermediate density nematic phase and second from the nematic phase to a high density re-entrant disordered phase. When the coordination number is 4, both the phase transitions are continuous and in the mean field Ising universality class. For even coordination number larger than 4, the first transition is discontinuous while the nature of the second transition depends on the rod length k and the interaction parameters.

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“…For fixed fugacities z k1 and z k2 , the system reaches an equilibrium density ρ(z k1 , z k2 ), defined as the fraction of sites occupied by the rods. This algorithm is an adaptation of the scheme that was quite efficient in equilibrating systems of monodispersed long rods [30,49]. Variants of this algorithm have been used to study systems of hard rectangles [50][51][52], disks on square lattice [53] and mixtures of squares and dimers [55].…”

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Phase diagram of a bidispersed hard-rod lattice gas in two dimensions

Kundu¹,

Stilck²,

Rajesh³

2015

EPL

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-We obtain, using extensive Monte Carlo simulations, virial expansion and a highdensity perturbation expansion about the fully packed monodispersed phase, the phase diagram of a system of bidispersed hard rods on a square lattice. We show numerically that when the length of the longer rods is 7, two continuous transitions may exist as the density of the longer rods in increased, keeping the density of shorter rods fixed: first from a low-density isotropic phase to a nematic phase, and second from the nematic to a high-density isotropic phase. The difference between the critical densities of the two transitions decreases to zero at a critical density of the shorter rods such that the fully packed phase is disordered for any composition. When both the rod lengths are larger than 6, we observe the existence of two transitions along the fully packed line as the composition is varied. Low-density virial expansion, truncated at second virial coefficient, reproduces features of the first transition. By developing a high-density perturbation expansion, we show that when one of the rods is long enough, there will be at least two isotropic-nematic transitions along the fully packed line as the composition is varied. and adsorbed gas molecules on metal surfaces [11][12][13][14][15]. A system of hard sphero-cylinders in three-dimensional continuum undergoes a transition from an isotropic phase to an orientationally ordered nematic phase as density is increased. Further increase in density leads to a smectic phase with partial translational order and a solid phase [10,[16][17][18][19][20]. In two-dimensional continuum, a Kosterlitz-Thouless transition to a high-density phase with power law correlations may be observed [21][22][23][24]. Lattice models of hard rods, of interest to this paper, also have a rich phase diagram in two dimensions, while not much is known in three dimensions.

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A Monte Carlo algorithm for studying phase transition in systems of hard rigid rods

Cited by 30 publications

References 4 publications

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

Reentrant disordered phase in a system of repulsive rods on a Bethe-like lattice

Phase diagram of a bidispersed hard-rod lattice gas in two dimensions

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